Colbert, who now hosts “The Colbert Report” on Comedy Central, signed a five-year deal to take over the show, saying he “never dreamed” he’d have the honor.

“Simply being a guest on David Letterman’s show has been a highlight of my career. I never dreamed that I would follow in his footsteps, though everyone in late night follows Dave’s lead … I’m thrilled and grateful that CBS chose me,” Colbert said.

He joked, “Now, if you’ll excuse me, I have to go grind a gap in my front teeth.”

Colbert will retire his signature character, a faux-conservative talking head, and will work on “The Colbert Report” for eight more months.

CBS has not yet revealed whether the “Late Show” will be shot at its current home at the Ed Sullivan Theater, which is located on Broadway between 53rd and 54th.

But since he’s already based in New York City, it’s likely Colbert — and the “Late Show” — will remain in Manhattan.

CBS Chairman and CEO Les Moonves is thrilled the satirical funny man will take over, he said.

“Stephen Colbert is one of the most inventive and respected forces on television,” Moonves said.

“David Letterman’s legacy and accomplishments are an incredible source of pride for all of us here, and today’s announcement speaks to our commitment of upholding what he established for CBS in late night,” he added.

Letterman himself also praised Colbert as the right man for the job.

“Stephen has always been a real friend to me. I’m very excited for him, and I’m flattered that CBS chose him. I also happen to know they wanted another guy with glasses,” Letterman said.

It remains to be seen how the news will impact Craig Ferguson, who hosts the “Late Late Show,” which follows “Late Show” at 12:35 a.m.

Ferguson’s contract with CBS automatically gives Letterman’s empty chair to Ferguson if he wants it, while awarding him $5 million if he is passed over.

There’s also no word on how Comedy Central will fill the hole left when Colbert leaves “The Colbert Report,” the show he’s hosted since 2005

“Comedy Central is proud that the incredibly talented Stephen Colbert has been part of our family for nearly two decades,” the network said in a statement.

“We look forward to the next eight months of the ground-breaking ‘Colbert Report’ and wish Stephen the very best.”

Letterman announced his retirement on April 5 after a record-setting 21 years on the show.

Fans and showbiz types took to Twitter to cheer the choice on Thursday.

“Nobody on television right now is more talented than Stephen Colbert. CBS is lucky to have him” tweeted @julieklausner.

Comedian Kristen Schaal gushed, “@StephenAtHome! You will be the best at the desk! But I will deeply miss the Colbert Report.”

The airing date and location of the show will be announced “at a later date,” CBS said.

Stephen Colbert to be next host of "The Late Show"…press release coming

Is Stephen Colbert the right choice for the "Late Show"?

I'll never forget when Stephen Colbert had a DNA expert on his show going over Colbert's genes when he announced that there was a 75% chance that Colbert was a Jew. Suddenly the show went dark, literally dark, that was the end of the show.

Colbert is funny. Jews are funny. Colbert should not be ashamed of being a Jew if the geneology says he is. There are no Jewish gene removal kits available yet. If they were I would give him one free along with Mark Zuckerberg, Jim Cramer and a thousand other Jews who are ashamed of their glorious heritage.

@Ban Letterman didn't choose Colbert, CBS did. If it were Letterman's choice it would have been Ferguson, since he owns that show and would have continued to produce The Late Show. That is not what's happening here.

No, bad choice. Colbert Report is funny, but he is in character. You can't host the Late Show in character. If he starts being himself and breaks character, it will blow up in his face, as he is already established as that character. They should have stuck with Ferguson. Now they may lose him in his late time slot too.

@spragga benz I'm not crying over Craig Ferguson. He gets $5 million no matter what and he has never shown the kind of interest in Letterman's job that Fallon did in Leno's. As for Colbert, I'm kind of on the fence about it. It's a little unusual but not entirely out of the box and that is where CBS likes to stay. Remember, their target audience is significantly older than most if not all of the rest of the network channels. If they went with someone unexpected, the core audience would probably jump ship pretty quickly. I don't know who I would have wanted to see in Letterman's place, but of all the people rumored to step in Colbert isn't the worst choice in the world. Now that Colbert's spot on Comedy Central is up for grabs, how about having a woman in that spot like Tina Fey or someone equally as talented in the spoofy news category as she is.

@Joanna I'm with you on Ferguson. He's getting paid, so be professional, and maybe he will. That said, the reality is that he may get hurt feelings and then CBS has to deal with hiring another replacement. My worry with Colbert is that the audience for the Late Show may not be the same as for the Colbert Report, and he loses a lot of Dave's viewers; and also that celebrity guests may not be interested in being interviewed as part of a political satire. They are trying to promote their crap, and Colbert's act may overshadow it. I'd be with you on Tina fey replacing Colbert, but they likely couldn't afford her, and she likely wouldn't be interested. She might have been a better replacement for Dave actually.

@spragga benz@Trudy Disher Did you read the article? Colbert is not doing the same character, he's being himself, so there will not be political satire. "there is a difference between being a character and a phony" So, Colbert is a Phony or a character?

@Entity Xero@spragga benz@Trudy Disher Sorry, I think they added info to the article before my comments. Did not previously read that he will retire his character. That makes him a risky/unknown commodity, but I do think the show has a better chance to work like this. I was suggesting Colbert from Colbert Report was a character, not phoney.